Quantum error-correcting codes are an important coding technique used to protect quantum information from noise and errors. Recently, researchers have been increasingly interested in the study of quantum error-correcting codes. In order to provide more research ideas and methods on error-correcting codes, in this paper, we study a topological error-correcting code called \(\textrm{XYZ}^{2}\) , which is encoded similar to the Kitaev honeycomb model lattice. Designing efficient decoders for quantum error-correcting codes remains a challenge. Here, we use a reinforcement learning algorithm to decode the \(\textrm{XYZ}^{2}\) code, which considers only the logical states associated with the \(\textrm{XYZ}^{2}\) code during the decoding process when training the reward agent. Considering the complexity of the \(\textrm{XYZ}^{2}\) code lattice computation, the spin property of the code is exploited to transform the honeycomb qubit lattice into a square lattice, and then, deep convolutional networks and experience replay techniques are used to implement the decoding design. Under the depolarizing noise model, we evaluate the training accuracy at different code distance, and the decoder can achieve about 83.33% error correction accuracy. We measured the threshold performance of the \(\textrm{XYZ}^{2}\) code at the maximum code distance of 7 and 9, which are 0.19029 and 0.21936, respectively. Finally, we utilized the deep Q-network to improve the decoding accuracy and successfully improved the fidelity of the qubits from 0.21513 to 0.76609. Our study provides directions and ideas for the application of reinforcement learning decoding schemes to other topological quantum error-correcting codes.
